Fractions with the Same Numerator

Axel and Tank are training Tank’s new dogfish, Sparky. Using the same-sized treats, they each break it into equal parts and feed him the same number of parts, but Sparky always goes to Axel instead of Tank! They think they are feeding Sparky the same amount, but they will need to learn about "Fractions with the Same Numerator" to determine what is going on! Fractions with the same numerator have the same number of shaded parts, but may have different denominators, so we need to compare them closely. When the whole is the same, a smaller number in the denominator means the pieces will be larger since there is less to divide between. To prove this, we can use fraction bars to compare values. Let's use the fractions one half and one third as examples. The whole for both is the same size. They both have the same numerator: one. However, their denominators are different. To compare, draw a fraction bar to represent the first fraction. Next, shade the bar to represent one-half. Then, draw a fraction bar of identical size to represent the second fraction. Now, shade the bar to represent one-third. Finally, compare the shaded parts of both models. One-half has a denominator that is smaller than one-third, but the whole is divided into just two parts so the pieces are actually larger. When comparing fractions with the same numerator and whole, the one with the smaller denominator is actually larger. Let's try this again using Axel and Tank's dogfish treats. Axel has two-fourths of a treat for Sparky. Tank has two sixths. Let's compare by drawing a fraction bar to represent Axel's fraction. Next, shade the bar to show two-fourths. Then, draw a fraction bar of identical size to represent Tank's fraction. Now, shade the bar to show two-sixths. Finally, compare the shaded parts of both bars. Two-fourths has a denominator that is smaller than two-sixths, but the whole is divided into just four parts so the pieces are actually larger. Again, when comparing fractions with the same numerator and whole, the one with the smaller denominator is actually larger so Sparky swims to Axel! Let's try it once more! This time Axel has three-thirds of a treat for Sparky. Tank has three-fifths. Pause the video and predict who has the larger fraction to give Sparky. Let's check our work! First, draw and shade a fraction bar to represent Axel's fraction, three-thirds. Then, draw and shade a fraction bar to represent Tank's fraction, three-fifths. Finally, compare the shaded parts of both models. The shaded value of three-thirds is greater than three-fifths, so Sparky swims to Axel again! Now we know why Sparky always swims to Axel instead of Tank! Before they finish training for the day, let's remember: To compare the size of two fractions with the same whole and the same numerator: first, draw and shade a fraction bar to represent the first fraction. Then, draw and shade a fraction bar of identical size to represent the second fraction. Finally, compare the shaded parts of both bars. If two fractions with the same whole have the same numerator but different denominators, the fraction with the smaller denominator is actually larger. "I'm making certain that Sparkly swims to me this time!"